I have an question ? Has any one child /toddler gotten sick since they been started school or…

I have an question ? Has any one child /toddler gotten sick since they been started school or daycare cause my daughter Malia has been sick off in on since she started she will get better then out the blow her nose will start to run then she will cough in she will get really hot but then she won’t even have a fever I’m confused her doctor says it’s because she’s in daycare but how long does it take for to he use to it I think she’s been in daycare for about 2 in a half months any answers moms!!!???